How does the CAPTCHA system in the Stack Exchange platform work behind-the-scenes?

Specifically, after the system decides to display a challenge to the user, how is the result URL stored? Furthermore, in instances when a CAPTCHA is displayed during a form submission: how and where is the form data stored?

Edit: We already know that it uses ReCAPTCHA (based on many architecture blogposts/answers) - my question is about how the platform is structured around ReCAPTCHA; e.g. where the form data is stored.